In this section, we construct a suitable type of homotopy equivalence between the classical and deformed
Hopf fibrations. The concept of homotopy equivalence presented here is slightly different
from the one proposed by Kassel and Schneider [1]} in the sense that
for our purposes it is more convenient to work with a larger algebra
of complex-valued functions on the real line \(\mathbb {R}\)  than the one
given by the polynomial algebra \(\mathbb {C}[y]\)  in one generator \(y\) . In particular, we
would like the exponential functions \(y\mapsto {\rm e}^{{\rm i} c y}\) , for \(c\in \mathbb {R}\) ,
to be contained in this algebra in order to obtain a homotopy equivalence that relates
the exponentiated deformation parameter \(q = {\rm e}^{2\pi {\rm i} \theta }\)  to the classical value 1.
